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jalvesz committed Dec 5, 2023
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* Integrate github CICD
* Polish autodoc

# Elapsed time examples and precision
Warning: The following values are just references as to see how different can they be between different compilers. Actual speed-ups(downs) should be measured under the true use conditions to account for (lack-off) inlinement, etc etc. Results obtained using a Intel(R) Xeon(R) Gold 6226R CPU @ 2.90GHz 2.89 GHz.
<details>
<summary>WSL2 gfortran 13.2 > fpm test --flag "-cpp -O3 -march=native -flto"</summary>

| sum r32 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 1.0300 | 1.00 | 3.1511E-06 |
| kahan | 0.1200 | 8.58 | 9.5367E-08 |
| chunk | 0.0900 | 11.44 | 1.0824E-07 |

| sum r64 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 1.2100 | 1.00 | 5.6974E-15 |
| kahan | 0.4300 | 2.81 | 1.3278E-16 |
| chunk | 0.1100 | 11.00 | 2.3359E-16 |

| sum r32 mask | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 1.2300 | 1.00 | 1.6180E-06 |
| kahan | 4.3400 | 0.28 | 8.3327E-08 |
| chunk | 0.3800 | 3.24 | 8.8394E-08 |

| sum r64 mask | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 3.8600 | 1.00 | 2.9463E-15 |
| kahan | 4.1950 | 0.92 | 6.8723E-17 |
| chunk | 0.4200 | 9.19 | 1.1879E-16 |

| dot r32 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 1.2100 | 1.00 | 3.2994E-06 |
| kahan | 0.2300 | 5.26 | 9.8348E-08 |
| chunk | 0.1200 | 10.08 | 1.1307E-07 |

| dot r64 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 1.1900 | 1.00 | 5.9648E-15 |
| kahan | 0.4400 | 2.70 | 1.2812E-16 |
| chunk | 0.0900 | 13.22 | 2.2760E-16 |

| trigo | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| fsin r32 | 0.5280 | 7.54 | 3.0972E-07 |
| fsin r64 | 0.9320 | 8.76 | 3.9779E-16 |
| facos r32 | 0.3080 | 20.87 | 2.9135E-05 |
| facos r64 | 0.5960 | 15.90 | 2.1557E-14 |

| hyperb | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| ftanh r32 | 1.7280 | 10.07 | 7.4200E-08 |
| ftanh r64 | 1.9360 | 9.32 | 1.3282E-09 |
| ferf r32 | 0.4760 | 31.71 | 9.6432E-08 |
| ferf r64 | 0.7640 | 18.42 | 9.6298E-08 |

| rsqrt | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| frsqrt r32 | 0.3480 | 1.06 | 9.4399E-04 |
| frsqrt r64 | 0.6320 | 2.23 | 8.6268E-04 |
</details>

<details>
<summary>WSL2 nvfortran 23.9 > fpm test --flag "-Mpreprocess -fast -Minline"</summary>

| sum r32 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.1000 | 1.00 | 1.1295E-07 |
| kahan | 1.2500 | 0.08 | 9.8169E-08 |
| chunk | 0.0700 | 1.43 | 7.0930E-08 |

| sum r64 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.1400 | 1.00 | 3.8969E-16 |
| kahan | 1.6300 | 0.09 | 1.2623E-16 |
| chunk | 0.2500 | 0.56 | 1.8996E-16 |

| sum r32 mask | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.1700 | 1.00 | 2.0742E-07 |
| kahan | 5.5650 | 0.03 | 8.1956E-08 |
| chunk | 0.2550 | 0.67 | 5.8889E-08 |

| sum r64 mask | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.3600 | 1.00 | 3.8136E-16 |
| kahan | 5.7750 | 0.06 | 6.2839E-17 |
| chunk | 0.4400 | 0.82 | 8.5598E-17 |

| dot r32 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.1400 | 1.00 | 1.1426E-07 |
| kahan | 1.9700 | 0.07 | 9.7811E-08 |
| chunk | 0.1700 | 0.82 | 7.1764E-08 |

| dot r64 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.2400 | 1.00 | 3.9246E-16 |
| kahan | 1.8700 | 0.13 | 1.3178E-16 |
| chunk | 0.4100 | 0.59 | 1.9129E-16 |

| trigo | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| fsin r32 | 0.0160 | 726.00 | 1.0325E-07 |
| fsin r64 | 0.0280 | 388.86 | 5.0118E-17 |
| facos r32 | 0.0120 | 466.67 | 1.0563E-06 |
| facos r64 | 0.0200 | 390.60 | 3.7996E-15 |

| hyperb | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| ftanh r32 | 0.0240 | 676.67 | 5.3264E-08 |
| ftanh r64 | 0.0080 | 1595.00 | 1.3282E-09 |
| ferf r32 | 0.0040 | 4851.00 | 9.1205E-08 |
| ferf r64 | 0.0320 | 549.62 | 9.6298E-08 |

| rsqrt | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| frsqrt r32 | 16.5480 | 0.02 | 9.4387E-04 |
| frsqrt r64 | 15.8280 | 0.09 | 8.6745E-04 |

</details>

<details>
<summary>WSL2 ifort 2021.10.0 > fpm test --flag "-fpp -O3 -xHost -ipo"</summary>

| sum r32 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.0700 | 1.00 | 6.2262E-08 |
| kahan | 0.2400 | 0.29 | 9.4564E-08 |
| chunk | 0.1000 | 0.70 | 7.0930E-08 |

| sum r64 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.0800 | 1.00 | 1.9862E-16 |
| kahan | 0.5200 | 0.15 | 1.2867E-16 |
| chunk | 0.1400 | 0.57 | 2.0384E-16 |

| sum r32 mask | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.2000 | 1.00 | 2.0568E-07 |
| kahan | 0.2150 | 0.93 | 7.7122E-08 |
| chunk | 0.1450 | 1.38 | 6.7770E-08 |

| sum r64 mask | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.2150 | 1.00 | 1.9040E-16 |
| kahan | 0.4400 | 0.49 | 7.0610E-17 |
| chunk | 0.3700 | 0.58 | 8.5154E-17 |

| dot r32 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.0700 | 1.00 | 6.2031E-08 |
| kahan | 0.2100 | 0.33 | 1.0544E-07 |
| chunk | 0.0500 | 1.40 | 7.1526E-08 |

| dot r64 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.2200 | 1.00 | 6.3782E-16 |
| kahan | 0.4600 | 0.48 | 2.4047E-16 |
| chunk | 0.1200 | 1.83 | 1.8829E-16 |

| trigo | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| fsin r32 | 0.3560 | 1.26 | 1.9746E-07 |
| fsin r64 | 0.9280 | 1.38 | 7.5661E-17 |
| facos r32 | 0.3200 | 2.01 | 3.0743E-06 |
| facos r64 | 0.6520 | 3.36 | 6.3642E-15 |

| hyperb | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| ftanh r32 | 0.3960 | 3.70 | 1.1537E-08 |
| ftanh r64 | 0.6760 | 5.17 | 1.3282E-09 |
| ferf r32 | 0.3360 | 2.50 | 1.0924E-07 |
| ferf r64 | 0.8440 | 2.18 | 9.6298E-08 |

| rsqrt | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| frsqrt r32 | 0.2600 | 1.31 | 9.4032E-04 |
| frsqrt r64 | 0.6360 | 2.27 | 8.7360E-04 |
</details>

<details>
<summary>Windows ifx 2023.2.0 > fpm test --flag "-fpp -O3 -xHost -ipo"</summary>

| sum r32 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.3200 | 1.00 | 8.4376E-07 |
| kahan | 1.0300 | 0.31 | 8.7321E-08 |
| chunk | 0.4800 | 0.67 | 8.7082E-08 |

| sum r64 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 1.1200 | 1.00 | 5.7371E-15 |
| kahan | 0.9400 | 1.19 | 1.9507E-16 |
| chunk | 0.5600 | 2.00 | 1.9418E-16 |

| sum r32 mask | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 2.2700 | 1.00 | 1.5584E-06 |
| kahan | 4.4750 | 0.51 | 9.1434E-08 |
| chunk | 4.7200 | 0.48 | 8.7559E-08 |

| sum r64 mask | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 2.1750 | 1.00 | 2.9075E-15 |
| kahan | 4.7550 | 0.46 | 1.0636E-16 |
| chunk | 4.0250 | 0.54 | 1.0525E-16 |

| dot r32 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.2600 | 1.00 | 7.9530E-07 |
| kahan | 1.3800 | 0.19 | 6.8307E-08 |
| chunk | 0.4900 | 0.53 | 6.9737E-08 |

| dot r64 | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| intrinsic | 0.6200 | 1.00 | 2.9848E-15 |
| kahan | 1.4200 | 0.44 | 1.8197E-16 |
| chunk | 0.5800 | 1.07 | 1.8330E-16 |

| trigo | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| fsin r32 | 3.4640 | 0.47 | 1.3924E-07 |
| fsin r64 | 3.2320 | 1.31 | 1.0296E-15 |
| facos r32 | 1.3960 | 5.22 | 3.1710E-05 |
| facos r64 | 1.4080 | 6.28 | 5.2928E-13 |

| hyperb | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| ftanh r32 | 2.8280 | 1.22 | 2.3012E-08 |
| ftanh r64 | 2.6280 | 2.97 | 1.3282E-09 |
| ferf r32 | 3.8600 | 1.57 | 3.0995E-07 |
| ferf r64 | 3.9600 | 5.67 | 9.6298E-08 |

| rsqrt | <time> [ns/eval] | Speed-Up | relative error |
|--------------|------------------|----------|-----------------|
| frsqrt r32 | 1.6640 | 0.19 | 9.4038E-04 |
| frsqrt r64 | 1.4320 | 0.96 | 8.7360E-04 |
</details>

# Acknowledgement

* Compilation of this library was possible thanks to [Transvalor S.A.](https://www.transvalor.com/en/homepage) research activities.
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